ORBi Collection: Mathematics
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Valid inequalities for the single arc design problem with set-ups
http://hdl.handle.net/2268/175191
Title: Valid inequalities for the single arc design problem with set-ups
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<br/>Author, co-author: Agra, Agostinho; Doostmohammadi, Mahdi; Louveaux, Quentin
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<br/>Abstract: We consider a mixed integer set which generalizes two well-known sets: the single node fixed- charge network set and the single arc design set. Such set arises as a relaxation of feasible sets of general mixed integer problems such as lot-sizing and network design problems.
We derive several families of valid inequalities that, in particular, generalize the arc resid- ual capacity inequalities and the flow cover inequalities. For the constant capacitated case we provide an extended compact formulation and give a partial description of the convex hull in the original space which is exact under a certain condition. By lifting some basic inequalities we provide some insight on the difficulty of obtaining such a full polyhedral description for the constant capacitated case. Preliminary computational results are presented.Wed, 17 Dec 2014 08:39:56 GMTDo the properties of an $S$-adic representation determine factor complexity?
http://hdl.handle.net/2268/174955
Title: Do the properties of an $S$-adic representation determine factor complexity?
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<br/>Author, co-author: Durand, Fabien; Leroy, Julien; Richomme, Gwenaël
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<br/>Commentary: 3032389Thu, 11 Dec 2014 17:11:27 GMTA combinatorial proof of $S$-adicity for sequences with linear complexity
http://hdl.handle.net/2268/174954
Title: A combinatorial proof of $S$-adicity for sequences with linear complexity
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<br/>Author, co-author: Leroy, Julien; Richomme, Gwenaël
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<br/>Commentary: 3083467Thu, 11 Dec 2014 17:04:37 GMTSome improvements of the S-adic conjecture
http://hdl.handle.net/2268/174953
Title: Some improvements of the S-adic conjecture
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<br/>Author, co-author: Leroy, Julien
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<br/>Commentary: 2845508 (2012j:68231)Thu, 11 Dec 2014 17:02:44 GMT$S$-adic conjecture and Bratteli diagrams
http://hdl.handle.net/2268/174952
Title: $S$-adic conjecture and Bratteli diagrams
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<br/>Author, co-author: Durand, Fabien; Leroy, Julien
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<br/>Commentary: 2996779Thu, 11 Dec 2014 17:01:04 GMTAn $S$-adic characterization of minimal subshifts with first difference of complexity $1 p(n+1)-p(n)\le2$
http://hdl.handle.net/2268/174951
Title: An $S$-adic characterization of minimal subshifts with first difference of complexity $1 p(n+1)-p(n)\le2$
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<br/>Author, co-author: Leroy, Julien
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<br/>Commentary: 3214265Thu, 11 Dec 2014 16:58:46 GMTAn analogue of Cobham's theorem for graph directed iterated function systems
http://hdl.handle.net/2268/174950
Title: An analogue of Cobham's theorem for graph directed iterated function systems
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<br/>Author, co-author: Charlier, Emilie; Leroy, Julien; Rigo, MichelThu, 11 Dec 2014 16:54:44 GMTAcyclic, connected and tree sets
http://hdl.handle.net/2268/174949
Title: Acyclic, connected and tree sets
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<br/>Author, co-author: Berthé, Valérie; De Felice, Clelia; Dolce, Francesco; Leroy, Julien; Perrin, Dominique; Reutenauer, Christophe; Rindone, GiuseppinaThu, 11 Dec 2014 16:49:20 GMTMaximal bifix decoding
http://hdl.handle.net/2268/174946
Title: Maximal bifix decoding
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<br/>Author, co-author: Berthé, Valérie; De Felice, Clelia; Dolce, Francesco; Leroy, Julien; Perrin, Dominique; Reutenauer, Christophe; Rindone, GiuseppinaThu, 11 Dec 2014 16:46:38 GMTBifix codes and interval exchanges
http://hdl.handle.net/2268/174945
Title: Bifix codes and interval exchanges
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<br/>Author, co-author: Berthé, Valérie; De Felice, Clelia; Dolce, Francesco; Leroy, Julien; Perrin, Dominique; Reutenauer, Christophe; Rindone, GiuseppinaThu, 11 Dec 2014 16:43:00 GMTThe finite index basis property
http://hdl.handle.net/2268/174944
Title: The finite index basis property
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<br/>Author, co-author: Berthé, Valérie; De Felice, Clelia; Dolce, Francesco; Leroy, Julien; Perrin, Dominique; Reutenauer, Christophe; Rindone, GiuseppinaThu, 11 Dec 2014 16:38:59 GMTBoolean Functions for Classification: Logical Analysis of Data
http://hdl.handle.net/2268/174887
Title: Boolean Functions for Classification: Logical Analysis of Data
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<br/>Author, co-author: Crama, YvesWed, 10 Dec 2014 16:36:52 GMTA classification of barycentrically associative polynomial functions
http://hdl.handle.net/2268/174500
Title: A classification of barycentrically associative polynomial functions
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<br/>Author, co-author: Marichal, Jean-Luc; Mathonet, Pierre; Tomaschek, Jörg
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<br/>Abstract: We describe the class of polynomial functions which are barycentrically associative over an infinite commutative integral domain.Fri, 28 Nov 2014 12:43:29 GMTOn modular decompositions of system signatures
http://hdl.handle.net/2268/174493
Title: On modular decompositions of system signatures
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<br/>Author, co-author: Marichal, Jean-Luc; Mathonet, Pierre
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<br/>Abstract: Considering a semicoherent system made up of $n$ components having i.i.d. continuous lifetimes, Samaniego defined its structural signature as the $n$-tuple whose $k$-th coordinate is the probability that the $k$-th component failure causes the system to fail. This $n$-tuple, which depends only on the structure of the system and not on the distribution of the component lifetimes, is a very useful tool in the theoretical analysis of coherent systems.
It was shown in two independent recent papers how the structural signature of a system partitioned into two disjoint modules can be computed from the signatures of these modules. In this work we consider the general case of a system partitioned into an arbitrary number of disjoint modules organized in an arbitrary way and we provide a general formula for the signature of the system in terms of the signatures of the modules.
The concept of signature was recently extended to the general case of semicoherent systems whose components may have dependent lifetimes. The same definition for the $n$-tuple gives rise to the probability signature, which may depend on both the structure of the system and the probability distribution of the component lifetimes. In this general setting, we show how under a natural condition on the distribution of the lifetimes, the probability signature of the system can be expressed in terms of the probability signatures of the modules. We finally discuss a few situations where this condition holds in the non-i.i.d. and nonexchangeable cases and provide some applications of the main results.Fri, 28 Nov 2014 08:58:54 GMTRegularity of functions: Genericity and multifractal analysis
http://hdl.handle.net/2268/174112
Title: Regularity of functions: Genericity and multifractal analysis
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<br/>Author, co-author: Esser, Céline
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<br/>Abstract: As surprising as it may seem, there exist functions of C∞(R) which are nowhere analytic. When such an unexpected object is found, a natural question is to ask whether many similar ones may exist. A classical technique is to use the Baire category theorem and the notion of residuality. This notion is purely topological and does not give any information about the measure of the set of objects satisfying such a property. In this
purpose, the notion of prevalence has been introduced. Moreover, one could also wonder whether large algebraic
structures of such objects can be constructed. This question is formalized by the notion of lineability.
The first objective of the thesis is to go further into the study of nowhere analytic functions. It is known that the set of nowhere analytic functions is residual and lineable in C∞([0, 1]). We prove that the set of nowhere analytic functions is also prevalent in C∞([0, 1]). Those results of genericity are then generalized using Gevrey classes, which can be seen as intermediate between the space of analytic functions and the space of infinitely differentiable functions. We also study how far such results of genericity could be extended to spaces of ultradifferentiable functions, defined using weight sequences or using weight functions.
The second main objective is to study the pointwise regularity of functions via their multifractal spectrum. Computing the multifractal spectrum of a function using directly its definition is an unattainable goal in most of the practical cases, but there exist heuristic methods, called multifractal formalisms, which allow to estimate this spectrum and which give satisfactory results in many situations. The Frisch-Parisi conjecture, classically used and based on Besov spaces, presents two disadvantages: it can only hold for spectra that are concave and
it can only yield the increasing part of spectra. Concerning the first problem, the use of Snu spaces allows to deal with non-concave increasing spectra. Concerning the second problem, a generalization of the Frisch-Parisi conjecture obtained by replacing the role played by wavelet coefficients by wavelet leaders allows to recover the decreasing part of concave spectra.
Our purpose in this thesis is to combine both approaches and define a new formalism derived from large deviations based on statistics of wavelet leaders. As expected, we show that this method yields non-concave spectra and is not limited to their increasing part. From the theoretical point of view, we prove that this formalism is more efficient than the previous wavelet-based multifractal formalisms. We present the underlying function space and endow it with a topology.Wed, 19 Nov 2014 15:02:58 GMTDistribution and robustness of a distance-based multivariate coefficient of variation
http://hdl.handle.net/2268/173750
Title: Distribution and robustness of a distance-based multivariate coefficient of variation
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<br/>Author, co-author: Aerts, Stéphanie
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<br/>Abstract: When one wants to compare the homogeneity of a characteristic in several popula-
tions that have di erent means, the advocated statistic is the univariate coe cient of variation.
However, in the multivariate setting, comparing marginal coe cients may be inconclusive.
Therefore, several extensions that summarize multivariate relative dispersion in one single in-
dex have been proposed in the literature (see Albert & Zhang, 2010, for a review).
In this poster, focus is on a particular extension, due to Voinov & Nikulin (1996), based on the
Mahalanobis distance between the mean and the origin of the design space. Some arguments
are outlined for justifying this choice. Then, properties of its sample version under elliptical
symmetry are discussed. Under normality, this estimator is shown to be biased at nite samples.
In order to overcome this drawback, two bias corrections are proposed.
Moreover, the empirical estimator also su ers from a lack of robustness, which is illustrated
by means of in uence functions. A robust counterpart based on the Minimum Covariance
Determinant estimator is advocated.Mon, 10 Nov 2014 11:09:42 GMTCorner asymptotics of the magnetic potential in the eddy-current model
http://hdl.handle.net/2268/173509
Title: Corner asymptotics of the magnetic potential in the eddy-current model
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<br/>Author, co-author: Dauge, Monique; Dular, Patrick; Krähenbühl, Laurent; Péron, Victor; Perrussel, Ronan; Poignard, Clair
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<br/>Abstract: In this paper, we describe the scalar magnetic potential in the vicinity of a corner of a conducting body embedded in a dielectric medium in a bidimensional setting. We make explicit the corner asymptotic expansion for this potential as the distance to the corner goes to zero. This expansion involves singular functions and singular coefficients. We introduce a method for the calculation of the singular functions near the corner and we provide two methods to compute the singular coefficients: the method of moments and the method of quasi-dual singular functions. Estimates for the convergence of both approximate methods are proven. We eventually illustrate the theoretical results with finite element computations. The specific non-standard feature of this problem lies in the structure of its singular functions: They have the form of series whose first terms are harmonic polynomials and further terms are genuine non-smooth functions generated by the piecewise constant zeroth order term of the operator.Sat, 01 Nov 2014 23:20:02 GMTAbelian bordered factors and periodicity
http://hdl.handle.net/2268/173420
Title: Abelian bordered factors and periodicity
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<br/>Author, co-author: Charlier, Emilie; Harju, Tero; Puzynina, Svetlana; Zamboni, Luca
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<br/>Abstract: A finite word is bordered if it has a non-empty proper prefix which is equal to its suffix, and unbordered otherwise. Ehrenfeucht and Silberger proved that an infinite word is (purely) periodic if and only if it contains only finitely many unbordered factors. We are interested in an abelian modification of this fact. Namely, we have the following question: Let w be an infinite
word such that all sufficiently long factors are abelian bordered. Is w (abelian) periodic? We also consider a weakly abelian modification of this question, when only the frequencies of letters are taken into account. Besides that, we answer a question of Avgustinovich, Karhumaki and Puzynina concerning abelian central factorization theorem.Tue, 28 Oct 2014 09:44:42 GMTThe freeness problem for products of matrices defined on bounded languages
http://hdl.handle.net/2268/173417
Title: The freeness problem for products of matrices defined on bounded languages
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<br/>Author, co-author: Charlier, Emilie; Honkala, Juha
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<br/>Abstract: In this talk, I presented a joint work with Juha Honkala. We study the freeness problem for matrix semigroups. We show that the freeness problem is decidable for upper-triangular 2x2 matrices with rational entries when the products are restricted to certain bounded languages. We also show that this problem becomes undecidable for large enough matrices.Tue, 28 Oct 2014 09:31:34 GMTInfinite self-shuffling words
http://hdl.handle.net/2268/173414
Title: Infinite self-shuffling words
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<br/>Author, co-author: Charlier, Emilie; Kamae, Teturo; Puzynina, Svetlana; Zamboni, Luca
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<br/>Abstract: In this paper we introduce and study a new property of infinite words: An infinite word x, with values in a finite set A, is said to be k-self-shuffling (k≥2) if there exists a shuffle of k copies of x which produces x. We are particularly interested in the case k=2, in which case we say x is self-shuffling. This property of infinite words is shown to be independent of the complexity of the word as measured by the number of distinct factors of each length. Examples exist from bounded to full complexity. It is also an intrinsic property of the word and not of its language (set of factors). For instance, every aperiodic word contains a non-self-shuffling word in its shift orbit closure. While the property of being self-shuffling is a relatively strong condition, many important words arising in the area of symbolic dynamics are verified to be self-shuffling. They include for instance the Thue–Morse word fixed by the morphism 0↦01, 1↦10. As another example we show that all Sturmian words of intercept 0<ρ<1 are self-shuffling (while those of intercept ρ=0 are not). Our characterization of self-shuffling Sturmian words can be interpreted arithmetically in terms of a dynamical embedding and defines an arithmetic process we call the stepping stone model. One important feature of self-shuffling words stems from their morphic invariance: The morphic image of a self-shuffling word is self-shuffling. This provides a useful tool for showing that one word is not the morphic image of another. In addition to its morphic invariance, this new notion has other unexpected applications particularly in the area of substitutive dynamical systems. For example, as a consequence of our characterization of self-shuffling Sturmian words, we recover a number theoretic result, originally due to Yasutomi, on a classification of pure morphic Sturmian words in the orbit of the characteristic.Tue, 28 Oct 2014 09:16:27 GMT